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Lecture# Complexity of Algorithms: Sorting Methods

Description

This lecture covers the complexity of algorithms, focusing on sorting methods. It discusses the sorting problem, various sorting algorithms like quick sort and insertion sort, and compares their efficiency. The instructor explains the concept of total order relation, the importance of sophisticated sorting for large datasets, and the detailed resolution of the insertion sort algorithm. Additionally, it analyzes worst-case scenarios for sorting algorithms and provides practical insights on algorithm design and efficiency comparison. The lecture concludes with a comparison between linear search and dichotomous search in ordered lists, emphasizing the relationship between algorithms and data representations.

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In course

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Related concepts (61)

CS-119(c): Information, Computation, Communication

L'objectif de ce cours est d'introduire les étudiants à la pensée algorithmique, de les familiariser avec les fondamentaux de l'Informatique et de développer une première compétence en programmation (

Sorting algorithm

In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output.

Merge sort

In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948.

Bubble sort

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

Insertion sort

Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time by comparisons. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. However, insertion sort provides several advantages: Simple implementation: Jon Bentley shows a three-line C/C++ version that is five lines when optimized. Efficient for (quite) small data sets, much like other quadratic (i.e.

Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

Related lectures (55)

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Recursive Algorithms: Induction & SortingCS-101: Advanced information, computation, communication I

Explores induction, recursion, and sorting algorithms, including merge sort and the proof of correctness for recursive algorithms.

Complexity & Induction: Algorithms & ProofsCS-101: Advanced information, computation, communication I

Explores worst-case complexity, mathematical induction, and algorithms like binary search and insertion sort.

Recursive Algorithms: Induction & SortingCS-101: Advanced information, computation, communication I

Covers induction, recursion, sorting algorithms, and the merge sort complexity in computer science.

Algorithm Complexity: Insertion SortCS-119(c): Information, Computation, Communication

Explores algorithm complexity, specifically the insertion sort method and its design strategy compared to other sorting algorithms.